In a 1972 article, Janet Nelson argued that medieval heresy  arose from a “crisis of theodicy” that arose because of an increasingly unstable and dislocated society.  Mixed with these motives were worries about purity: Heretical groups believed themselves to be liberating themselves from the corruptions of the mainstream church: “Cathar dualism maybe seen as a typically sectarian response, combining affirmation of the purityand internal solidarity of a new group with rejection of corrupt external institutions; the gulf between them is mirrored in the cosmic polarity.”

Church authorities, of course, saw things the other way round.  Innocent III commended Simon de Montfort for his campaigns against the Cathars in Languedoc as an effective purgation and medication of the church:

“The hand of God, beginning at last to destroy [destruere] the mighty who gloried in their malice and iniquity, hath now made them migrate from their tabernacles in wondrous wise. For God hath mercifully purged his people’s land; and the pest of heretical wickedness, which had grown like a cancer and infested almost the whole of Provence, is being deadened and driven away -  mortificata depellitur . . . . [U]rge your flocks by zealous and sedulous preaching and exhortation, to give devout obedience to God and timely help to the Church both personally and through what is theirs, in order to extirpate the remnants of this pest; since like that hydra which is said to have multiplied its heads by their very loss, these also, if neglected, might revive the more grievously.”

In the section on heresy in the Summa , Thomas quoted Jerome to a similar effect: “Cut off the decayed flesh, expel the mangy sheep from the fold, lest the whole house, the whole paste, the whole body, the whole flock burn, perish, rot, die. Arius was but a single spark in Alexandria, but as it was not at once put out,the whole world was laid waste by his flame.”